New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities
New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities
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DOI：
10.1088/1367-2630/16/5/055014
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发表时间：
2014-05-28
影响因子：
3.3
通讯作者：
Collins, Lance R.
中科院分区：
文献类型：
--
作者：
Bragg, Andrew D.;Collins, Lance R.
这两部分系列的第一部分比较了径向分布函数（RDF）的两种理论，RDF是各向同性湍流中惯性颗粒聚集的统计测量。在第二部分中，我们将对比各向同性湍流中惯性粒子相对速度的三个理论模型，其中一个是Zaichik等人（2009 New. J.Phys.11103018），第二种由Pan等人（2010 J.Fluid Mech.66173），第三种由Gustavsson等人（2011 Phys.Rev.E.J.Phys.11103018）。84 045304）。我们发现，在一般情况下，他们描述的相对速度在定性上相似的方式，捕捉的非局部动力学的形成焦散和非光滑的标度行为的耗散范围内的影响。然后，我们将理论预测与直接数值模拟数据进行比较，发现虽然它们一致地捕获了数据的定性行为，但它们在数量上不同，并且我们讨论了每个理论中可能的误差来源。最后，我们考虑如何Zaichik等人的理论预测，焦散线的形成修改的RDF的形式，并表明，该理论描述的行为的RDF的粒子的响应时间尺度与惯性范围的时间尺度的湍流。
Part I of this two-part series compared two theories for the radial distribution function (RDF), a statistical measure of the clustering of inertial particles in isotropic turbulence. In Part II, we will contrast three theoretical models for the relative velocities of inertial particles in isotropic turbulence, one by Zaichik et al (2009 New. J. Phys. 11 103018), the second by Pan et al (2010 J. Fluid Mech. 661 73) and the third by Gustavsson et al (2011 Phys. Rev. E. 84 045304). We find that in general they describe the relative velocities in qualitatively similar ways, capturing the influence of the non-local dynamics on the formation of caustics and non-smooth scaling behavior in the dissipation range. We then compare the theoretical predictions with direct numerical simulation data and find that although they capture the qualitative behavior of the data consistently, they differ quantitatively, and we discuss the possible sources of error in each of the theories. Finally, we consider how the Zaichik et al theory predicts that the formation of caustics modifies the form of the RDF, and show that the theory describes the behavior of the RDF for particles whose response time scales with the inertial range time scales of the turbulence.